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arXiv · 2606.00705

Locating a shortest vector in certain $2$-dimensional lattices

Guixian Zou
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Abstract

Let $a$, $m$ be positive integers, $1<a<m$, $\gcd(a,m)=1$. We determine the location of a shortest vector in the $2$-dimensional lattices $$ \Lambda(a,m) = \{(x, y)\in\mathbb{Z}\times\mathbb{Z}\mid ax + y\equiv 0~(\bmod\,m)\}. $$ This confirms a conjecture of Han Wu and Guangwu Xu.

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Guixian Zou. 2026-05-30. Locating a shortest vector in certain $2$-dimensional lattices. https://arxiv.org/abs/2606.00705

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